the diffusion equation is still obtained: 



q ^ ^ f40) 



Bakker has applied his theory to a number of idealized cases, in- 

 cluding the behavior of a sand beach near a groin, assuming 



°1 = ^2 



(41) 



q^ = q. 



The boundary conditions are: 



a. Initial condition (t = o) : y = y = o for o<x«» and t = o . 



b. Then, when t>o: 



(1) Xi - Y-y - o for x-^^ and o <t<°° (which implies an equilibri- 



um profile) 



(2) y = o for x = o 



(3) 1 = tana for x = o 



33r ^1 



The results are expressed in terms of lengthy power series, and are 

 represented graphically in Fig. 14. 



The case of equilibrium beach profiles between groins was also 

 investigated by Bakker (1970). 



Despite the complex refinement of the two-line theory, as initially 

 developed by Bakker, a number of phenomena that have significant in- 

 fluence on the beach profile are still neglected. Among these are: 



a. The influence of rip current near the groins is twofold: rip 

 currents transport material from beach to the offshore and cause wave 

 refraction . 



37 



